Use a CAS and Stokes' theorem to evaluate curl(F) · dS, where F(x, y, z) = 2yi + ej - arctan(x)k with S as a portion of paraboloid z = 9 - x - y cut off by the xy-plane oriented counterclockwise with upward pointing normal. (Round your answer to four decimal places.)

Q: Use Stokes' theorem to evaluate the surface integral I of the two-form w = dŋ, with n = (xz+ yz²) dæ…

A: η=(xz+yz2)dx+(sin(y)+z+5x)dy+xyz dzz=13-x2-y2,   z≥9 F→=xz+yz2i+(sin(y)+z+5x)j+xyzk z=9⇒9=13-x2-y2…

Q: Use Stokes' theorem to evaluate (V x F) - dS where F(x, y, z) = -6yzi + 6rzj + 5(x2 + y²)zk and S is…

A: Given that F(x,y,z)=-6yzi^ + 6xz j^+ 5(x2+y2)z k^ Calculating the curl,…

Q: Use Stoke's theorem to evaluate the integral curl F dS where S is the surface given by e1-a -y – 1,…

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Q: Let F Use Stokes' Theorem to evaluate F · dī, where C is the curve of intersection of the parabolic…

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Q: Let F = Use Stokes' Theorem to evaluate F dī, where Cis the curve of intersection of the parabolic…

A: Given F¯=xy,4z,6y We have to evaluate ∫CF¯⋅dr¯ by using stokes theorem, where C is the curve of…

Q: Use Stokes' Theorem to evaluate curl F· dS. F(x, y, z) = 6y cos(z) i + e\ sin(z) j + xeY k, S is the…

A: This question is about application Stokes theorem

Q: Use Stokes' theorem to evaluate curl(F) · dS. F(x, y, z) = exy cos(z)i + x2zj + xy k, S is the…

A: F(x, y, z) = exy cos (z) i + x2 z j + xy k

Q: Use Stokes' Theorem to find the circulation of F = 6yi + 5zj + 5xk around a circle C of radius 7…

A: According to Stoke's Theorem: ∮CF→⋅dr→=∬S(∇→×F→)⋅n^dS here n^ is the vector normal to  the surface S…

Q: Use Stokes' Theorem to evaluate curl F· dS. F(x, y, z) = tan-(x²yz²)i + x²yj + x²z?k, S is the cone…

A: The objective here is to evaluate: ∬ScurlF⋅dSWhere, Fx,y,z=tan−1x2yz2i+x2yj+x2z2k; and S is the cone…

Q: Use Stokes' Theorem to evaluate the integral: [cur S curl F. dS F(x,y,z)=ze' i+xcos (y) j+xzsin (y)…

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Q: Use Stokes' Theorem to evaluate curl F· dS. F(x, y, z) = zei + x cos(y)j + xz sin(y)k, S is the…

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Q: Use Stokes' Theorem to calculate the integral / curl F · dà where F = -5yi+ 5xj + (xy+4 cos z)k and…

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Q: Use Stokes' Theorem to evaluate F. dr where F(x, y, 2)æzî + 2ry} +3ryk where C is the boundary of…

A: According to the given information, it is required to use stokes theorem to evaluate the integral.

Q: Use Stokes' Theorem to evaluate F. dr where F(x, y, z) = xi + yj +Xx² + y² )k and C is the boundary…

A: Stokes theorem: ∮f→·dr→=∬S curl f→·n^ ds Given F(x, y, z)=xi + yj+9(x2+y2)k and C is the boundary of…

Q: Use Stokes' Theorem to evaluate F. dr, where F(x, y, z) = xzi+ xyj+2xz k,•. and C is the boundary of…

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Q: Using Green’s theorem, evaluate the line integral ∮Cxydx+ (x+y)dy, where C is the curve bounding the…

A: Given: Where the components of the vector field are

Q: 3. Consider A(r) = (y, -x,0), and the line integral A• dr along the C boundary of the plane x + y +…

A: The given vector function is A(r)=(y,-x,0)., the line integral ∮CA·dr is along the boundary of the…

Q: Use Stokes' Theorem to evaluate || curl F. dS. F(x, y, z) = x² sin(z)i + y²j + xyk, S is the part of…

A: Here use the stokes theorem to find the integral of the function and given that the function…

Q: Given F(x, y, z) = xzi + 3yj + yzk be a vector function that passes through a surface S of z+x² + y?…

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Q: Use Stokes' theorem to evaluate curl F. dS, where F(x, y, z) = e*Y cos(z)i + x²zj + xyk, and S is…

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Q: Jse Stokes' Theorem to evaluate curl F· dS. F(x, y, z) = x2 sin(z)i + y?j + xyk, S is the part of…

A: Consider the vector field F⟨x,y,z⟩=x2sinzi+y2j+xyk S is the surface which is part of the…

Q: Use Stokes' Theorem to evaluate ∫∫ s  curl F. dS  F(x,y,z) = x2 sin zi +y2 j +xyK, S is the part of…

A: Given: F(x,y,z)=x2 sin z i + y2 j +xy k and S is the surface of paraboloid z=1-x2-y2, which is above…

Q: Let F = . Use Stokes' Theorem to evaluate curlF · d§ , where S is the part of the paraboloid z…

A: Given: F=-yz,xz,xy To Find: Use Stokes' Theorem to evaluate ∬Scurl F·dS, whereS is the part of the…

Q: Evaluate the surface integal [[Curl F.ñ dS for the Sur face and F=xt-y²+ (x+4+z)Ñ and C is the bo…

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Q: Use Stokes' theorem to evaluate E (wy – y) i – In z j+ (x+x²) k) · dr, where C is the intersection…

A: The required curve C(red) is shown as follows: The intersection gives a disc D bounded by curve C,…

Q: Use Stokes' theorem to evaluate curl F- ds. F(x, y, z) = ze'i + x cos(y)j + xz sin(y)k, S is the…

A: The given vector, F(x,y,z)=zeyi+xcos(y)j+xzsin(y)k Use Stokes theorem to find, ∬Scurl F. dS=∬∫curl…

Q: Given F(x, y, z) = xzi + 3yj + yzk be a vector function that passes through a surface S of z+x? + y?…

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Q: Use Stokes' Theorem to evaluate curl F. dS. F(x, y, z) = x2y3zi + sin(xyz)j + xyzk, S is the part of…

A: Stokes theorem: ∫∫ScurlF.dS=∫CF.dr

Q: Use Stokes' Theorem to evaluate |/ curl F. dS. F(x, y, z) = tan-(x²yz²)i + x²yj + x²z?k, S is the…

A: Stokes' Theorem:                                 ∮C F .dr =∬S curl F. dS Where C is the boundary of…

Q: Let F (x, y, z): = (x + 2y2, y + z2, z + 2x2), and let C be the curve that results from the…

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Q: Use Stokes' theorem to evaluate curl(F) · dS. F(x, y, z) = x² sin(z) i + yj + xyk, S is the part of…

A: Given that, And he paraboliod is The aim is to find The radius is 3. Take C is x(t)=cos t and…

Q: Use Stokes' Theorem to evaluate [[(curlF)•ndS where F(x,y,z) =x’i+z°j-y°k and o is that portion of…

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Q: 9) Use Stokes' Theorem to evaluate || curl (F)· dS where F(x, y, z) = (x sin z)i+(x)j+(xy)k and S is…

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Q: Use Stokes' Theorem to evaluate curl F · dS. F(x, y, z) = x2y3zi + sin(xyz)j + xyzk, S is the part…

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Q: Use Stokes' theorem to evaluate |/ curl(F) · ds. F(x, y, z) = x? sin(2) i + y?j + xyk, S is the part…

A: Use the formula of Stokes theorem and use the parameterization of curves to determine the values of…

Q: Use Stokes' Theorem to evaluate SSs curl F· dS. F(x,y,z) = x2z2 i + y²z² j + xyz k S is the part of…

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Q: Let F . F. dr, where Use Stokes' Theorem to evaluate C is the curve of intersection of the…

A: The given vector function: F→=<xy,2z,3y> To find ∫CF→.dr by using Stokes theorem. The Formula…

Q: Use Stokes' Theorem to evaluate curl F· ds. F(x, y, z) = ze'i + x cos(y)j + xz sin(y)k, S is the…

A: Stoke's theorem: The surface integral of the normal component of the curl of F is equal to the line…

Q: Let F = Use Stokes' Theorem to evaluate F. dī, where C is the curve of intersection of the…

A:

Q: Use Stokes theorem to evaluate ff.curl F.nds. where F = (xyz, x, e* cos z), while S is surface x² +…

A: Solution :

Q: . Evaluate the flux integral f. curl (z cos xi+ yj+ x sin y k) dS where S is the part of the outward…

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Q: Use Stokes' Theorem to evaluate  curl F · dS. F(x, y, z) = 6y cos(z) i + ex sin(z) j + xey k, S is…

A: From the given statement,

Q: Given F(x, y, z) = -yzį + xzj – xyzk be a vector function that passes through a surface S of z +x? +…

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Q: Use Stokes's Theorem to show that 0= [[ curl(F) - dS where F(r, Y, z) = (2, 2ry, x + y) and S is the…

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Q: Use Stokes' Theorem to evaluate curl F· dS. F(x, y, z) = x² sin(z)i + y²j + xyk, S is the part of…

A: Given problem is :

Q: Let F = . Use Stokes' Theorem to evaluate curlF · dS,where Sis the part of the paraboloid z = 10 –…

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Q: Evaluate the flux integral , curl (z cos x î + y j+ x sin y k) dS where S is the part of the outward…

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Q: Use Stokes' theorem to evaluate curl(F) · ds. F(x, y, z) = exYi + ej + xzk, Sis the half of the…

A: Given: F(x,y,z)=e4xy i+exz j+x2z k The half of ellipsoid 8x2+y2+8z2=8 To find:  ∫S∫curl(F). dS Use…

Q: Let F = · Use Stokes' Theorem to evaluate curi curlF · d§, where S is the part of the paraboloid z…

A: here i had written stokes theorem and done some basic calculation to find the curve of intersection…

Q: Use Stokes' Theorem to evaluate curl F. dS. F(x, y, z) = exY cos(z)i + x²zj + xyk, S is the…

A: Given F→x,y,z=exycoszi^+x2zj^+xyk^ We have t find the integral ∬ScurlF→⋅dS, where S is the…